Finite Group Databasebeta

← Prev (#37528744) Next (#37528746) →

C2×C3×C7×C5⋊D55 #37528745

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C7×C5⋊D55
unambiguous semidirect product(C2×C5)⋊(C3×C7×D55)
unambiguous semidirect product(C2×C11)⋊(C3×C7×C5⋊D5)

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, HallC52×C11 ⋊ C22×C3×C7
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C22×C7
HallC3×C52×C7 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×C5⋊D5
HallC3×C52 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×C5⋊D5
SylowC52 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C5⋊D55
commutator, cosocle, hypocenterC52×C11C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C52×C11
UCSC1 ◁ C2×C3×C7

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 556);